author  wenzelm 
Fri, 09 Nov 2001 00:00:53 +0100  
changeset 12110  f8b4b11cd79d 
parent 10467  e6e7205e9e91 
child 17441  5b5feca0344a 
permissions  rwrr 
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(* Title: CTT/arith 
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ID: $Id$ 
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
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Copyright 1991 University of Cambridge 
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Arithmetic operators and their definitions 

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Proves about elementary arithmetic: addition, multiplication, etc. 

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Tests definitions and simplifier. 

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*) 

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Arith = CTT + 

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consts "#+","","" :: "[i,i]=>i" (infixr 65) 
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"#*",div,mod :: "[i,i]=>i" (infixr 70) 

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12110
f8b4b11cd79d
eliminated old "symbols" syntax, use "xsymbols" instead;
wenzelm
parents:
10467
diff
changeset

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syntax (xsymbols) 
10467
e6e7205e9e91
xsymbol support for Pi, Sigma, >, : (membership)
paulson
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3837
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"op #*" :: [i, i] => i (infixr "#\\<times>" 70) 
e6e7205e9e91
xsymbol support for Pi, Sigma, >, : (membership)
paulson
parents:
3837
diff
changeset

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e6e7205e9e91
xsymbol support for Pi, Sigma, >, : (membership)
paulson
parents:
3837
diff
changeset

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syntax (HTML output) 
e6e7205e9e91
xsymbol support for Pi, Sigma, >, : (membership)
paulson
parents:
3837
diff
changeset

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"op #*" :: [i, i] => i (infixr "#\\<times>" 70) 
e6e7205e9e91
xsymbol support for Pi, Sigma, >, : (membership)
paulson
parents:
3837
diff
changeset

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rules 
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add_def "a#+b == rec(a, b, %u v. succ(v))" 
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diff_def "ab == rec(b, a, %u v. rec(v, 0, %x y. x))" 

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absdiff_def "ab == (ab) #+ (ba)" 
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mult_def "a#*b == rec(a, 0, %u v. b #+ v)" 

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mod_def "a mod b == rec(a, 0, %u v. rec(succ(v)  b, 0, %x y. succ(v)))" 
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div_def "a div b == rec(a, 0, %u v. rec(succ(u) mod b, succ(v), %x y. v))" 

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end 